Please refer to FIG. 1, which is a schematic diagram depicting the framework of a conventional variable gain amplifier 100. The variable gain amplifier 100 has an operational amplifier 110, a resistor set 120 having a plurality of serial-connected resistors Rf1, Rf2, . . . , Rfn, and a switch set 130 having a plurality of switches SW1, SW2, . . . , SWn corresponding to the resistors respectively. The switches are generally implemented with MOS transistors. Under such configuration of FIG. 1, a gain G of the variable gain amplifier 100 is given by: G=1+Rf/Rg, wherein Rf is a resistance seen between the output Vo and the inverting input (−) of the operational amplifier 110, while Rg is a resistance seen between the inverting input (−) of the operational amplifier 110 and a ground node Vag. Both the resistance Rf and Rg depend on the on/off state of the corresponding switches in the switch set 130. The conventional variable gain amplifier 100 can ensure a monotonic variation in gain, and can avoid nonlinear distortion and gain error caused by the MOS switches since there is no current flowing through the MOS switches.
However, since the signal at the non-inverting input (+) of the operational amplifier 110 varies with the input signal Vi and the input dynamic range of the operational amplifier 110 is comparatively small, the conventional variable gain amplifier 100 tends to suffer from more significant distortion. In addition, the conventional variable gain amplifier 100 cannot perform signal attenuation and possesses inferior gain accuracy.
Please refer to FIG. 2, which is a schematic diagram depicting the framework of another conventional variable gain amplifier 200. The variable gain amplifier 200 has an operational amplifier (OPA) 210, an input resistor Ri, a feedback resistor set 220 having a plurality of serial-connected resistors Rk1, Rk2, . . . , Rkn, and a switch set 230 having a plurality of switches Sk1, Sk2, . . . , Skn corresponding respectively to the resistors. The switches are generally implemented with MOS transistors. Under such configuration of FIG. 2, a gain G of the variable gain amplifier 100 is given by: G=Rk/Ri, wherein Rk is an equivalent resistance shown by the resistor set 220. As seen in FIG. 2, the non-inverting input (+) of the OPA 210 is fixed to a ground node Vag. Therefore, the OPA 210 tends to have smaller distortion.
However, since current will flow through the MOS switches in this framework, the nonlinearity of the MOS switch may incur signal distortion. Also, gain error may be induced by the impedance of the MOS switch. In addition, in FIG. 2 if the tolerable noise level is low, the input resistor Ri with a small impedance and the feedback resistors with small impedances are needed. However, when the impedances of the input resistor and the feedback resistors are of small values, the MOS switches with large equivalent resistances is required so as to reduce distortion and gain error. Unfortunately, when large-resistance MOS switches are adopted, the parasitic capacitors thereof tend to cause loop instability and substrate coupling issues.